No, because that is not how destiny knot works. According to Serebii the destiny knot works like this:
When this item is held by a Pokémon, if the holder becomes Infatuated, the Pokémon it is attracted to also becomes Infatuated.
As of Pokémon X & Y, this item, when attached to a Pokémon while breeding, will cause the baby Pokémon to inherit 5 IVs from its parents
Notice how it does not mention trading. Also, when trading for a Pokemon in the GTS, you will get the exact Pokemon the trainer put up. EVs, IVs, natures etc. One reason for dittos holding destiny knot in GTS could be that since dittos are used for breeding, trainers may add it to increase the value of it.
This and knowledge